Southampton manager Ronald Koeman hopes Morgan Schneiderlin's transfer saga is resolved soon after revealing the club rejected a "not serious" offer from Manchester United for the midfielder earlier on June.

The future of the France international at St Mary's has been under scrutiny since the summer of 2014, when he was heavily linked with Arsenal and Tottenham.

And United manager Louis van Gaal has now earmarked his signing as a top priority for the summer transfer window to cover to Michael Carrick after the French star attracted his attention during Southampton's impressive seventh-place finish in the Premier League last term.

The Telegraph recently revealed United made an initial bid of £20m ($31.1m) to secure his services, which was rejected as Southampton demand at least £25m to part ways with the Frenchman.

With Schneiderlin wanting to make the move to a Champions League side, The Guardian later reported Van Gaal's side were ready to make an improve bid to close the deal.

But Koeman has said United are yet to submit an improved bid for the player, while expressing his hope to resolve the situation soon in case he needs to sign a replacement.

"A lot of speculation, but two weeks ago we had a bid from Manchester United. It wasn't enough, it wasn't serious, and [there have been] no more bids till today [Monday]," Koeman said to reporters, as quoted by Sky Sports.

"I hope that if there is any business, that it will be soon because it's best for the player, best for us, we have to prepare ourselves if we sell the player.

Koeman, meanwhile, has not hidden Schneiderlin's intention to make a move to a bigger club but suggests the only way for him to leave is if another team meets Southampton's demands.

"Everybody knows the situation of Morgan. I understand the player – if he can get a big move to a big [club], I can understand it.

"I've had a lot of meetings with Morgan. I had a meeting last week, everybody knows his situation. But it's important for the player to do a good pre-season. And we will see what happens in the next few days. I don't talk about money, about numbers, it's not my business, it's up to the club."